Rearrange characters of a string to make it a concatenation of palindromic substrings

Given a string S consisting of lowercase alphabets, the task is to check whether the given string can be rearranged such that the string can be split into non-overlapping palindromic substrings of at least length 2. If found to be true, then print "Yes". Otherwise, print "No".

Examples:

Input: S = "aaaabbcdd"
Output: Yes
Explanation: Rearrange the given string S to “acaaabbdd”, which can be split into non-overlapping palindromic substrings "aca", "aa", "bb", "dd”.

Input: S = "ccddgggggefs"
Output: No

Approach: The given problem can be solved by rearranging the characters of the string into substrings of length 2, consisting of single distinct character. If there exists any character with odd frequency, then it place them in the middle of the palindromic substrings of length 2. 
Follow the steps below to solve the problem:

• Initialize an auxiliary array, say frequency[] of size 26, to store the frequency of every character present in the string S.
• Traverse the given string S and update the frequency of each character in the array frequency[].
• Initialize two variables, say odd and even both as 0, to store the frequency of odd elements and the number of palindromic substrings of length 2 formed.
• Traverse the array frequency[] and if the value of frequency[i] is greater than 0, then add the value (frequency[i] & 1) and (frequency[i] / 2) to the variable odd and even respectively.
• After completing the above steps, if the value of odd is at most even, then print "Yes". Otherwise, print "No".

Below is the implementation of the above approach:

// C++ program for the above approach

#include <bits/stdc++.h>
using namespace std;

// Function to check if a string can be
// modified such that it can be split into
// palindromic substrings of length >= 2
void canSplit(string& S)
{
    // Stores frequencies of characters
    vector<int> frequency(26, 0);

    int cnt_singles = 0;

    int k = 0;

    // Traverse the string
    for (int i = 0; i < S.length(); i++)

        // Update frequency
        // of each character
        frequency[S[i] - 'a']++;

    int odd = 0, eve = 0;

    // Traverse the frequency array
    for (int i = 0; i < 26; i++) {

        // Update values of odd and eve
        if (frequency[i]) {
            odd += (frequency[i] & 1);
            eve += frequency[i] / 2;
        }
    }

    // Print the result
    if (eve >= odd)
        cout << "Yes";
    else
        cout << "No";
}

// Driver Code
int main()
{
    string S = "aaabbbccc";
    canSplit(S);

    return 0;
}

// Java program for the above approach
import java.io.*;
import java.lang.*;
import java.util.*;

class GFG {

    // Function to check if a string can be
    // modified such that it can be split into
    // palindromic substrings of length >= 2
    static void canSplit(String S)
    {
        // Stores frequencies of characters
        int frequency[] = new int[26];

        int cnt_singles = 0;

        int k = 0;

        // Traverse the string
        for (int i = 0; i < S.length(); i++)

            // Update frequency
            // of each character
            frequency[S.charAt(i) - 'a']++;

        int odd = 0, eve = 0;

        // Traverse the frequency array
        for (int i = 0; i < 26; i++) {

            // Update values of odd and eve
            if (frequency[i] != 0) {
                odd += (frequency[i] & 1);
                eve += frequency[i] / 2;
            }
        }

        // Print the result
        if (eve >= odd)
            System.out.println("Yes");
        else
            System.out.println("No");
    }

    // Driver Code
    public static void main(String[] args)
    {

        String S = "aaabbbccc";
        canSplit(S);
    }
}

# Python3 program for the above approach

# Function to check if a string can be
# modified such that it can be split into
# palindromic substrings of length >= 2
def canSplit(S):

    # Stores frequencies of characters
    frequency = [0] * 26 

    cnt_singles = 0

    k = 0

    # Traverse the string
    for i in range(len(S)):

        # Update frequency
        # of each character
        frequency[ord(S[i]) - ord('a')] += 1

    odd = 0
    eve = 0

    # Traverse the frequency array
    for i in range(26):

        # Update values of odd and even
        if (frequency[i]):
            odd += (frequency[i] & 1)
            eve += frequency[i] // 2

    # Print the result
    if (eve >= odd):
        print("Yes")
    else:
        print("No")

# Driver Code
if __name__ == "__main__" :

    S = "aaabbbccc"
    
    canSplit(S)

# This code is contributed by AnkThon

// C# program for the above approach
using System;
public class GFG 
{

  // Function to check if a string can be
  // modified such that it can be split into
  // palindromic substrings of length >= 2
  static void canSplit(string S)
  {

    // Stores frequencies of characters
    int []frequency = new int[26];
    int cnt_singles = 0;
    int k = 0;

    // Traverse the string
    for (int i = 0; i < S.Length; i++)

      // Update frequency
      // of each character
      frequency[S[i] - 'a']++;

    int odd = 0, eve = 0;

    // Traverse the frequency array
    for (int i = 0; i < 26; i++) 
    {

      // Update values of odd and eve
      if (frequency[i] != 0)
      {
        odd += (frequency[i] & 1);
        eve += frequency[i] / 2;
      }
    }

    // Print the result
    if (eve >= odd)
      Console.WriteLine("Yes");
    else
      Console.WriteLine("No");
  }

  // Driver Code
  public static void Main(string[] args)
  {

    string S = "aaabbbccc";
    canSplit(S);
  }
}

// This code is contributed by AnkThon

<script>
    // Javascript program for the above approach

// Function to check if a string can be
// modified such that it can be split into
// palindromic substrings of length >= 2
function canSplit(S){

    // Stores frequencies of characters
    let frequency = new Array(26).fill(0)

    let cnt_singles = 0

    let k = 0

    // Traverse the string
    for(let i = 0; i < S.length; i++){

        // Update frequency
        // of each character
        frequency[S.charCodeAt(i) - 'a'.charCodeAt(0)] += 1
    }
    let odd = 0
    let eve = 0

    // Traverse the frequency array
    for(let i = 0;  i < 26; i++){

        // Update values of odd and eve
        if (frequency[i]){
            odd += (frequency[i] & 1)
            eve += frequency[i] // 2
        }
    }
    // document.write the result
    if (eve >= odd){
        document.write("Yes")
    }
    else{
        document.write("No")
    }
}

// Driver Code
 
    let S = "aaabbbccc"
    
    canSplit(S)

// This code is contributed by gfgking

</script>

Yes

Time Complexity: O(N)
Auxiliary Space: O(1)